Hidden Quadruplet in a Hexadoku
As has been said earlier, the probability of the occurrence of a hidden Quadruplet in a 9x9 puzzle is extremely low. Although that must be relativized.
Because many patterns are complementary to each other, the occurrence of a Hidden Quadruplet groupis, in principle, a very common occurrence. Imagine the following situation: In a logical unit three fields are filled in, while six are still empty. In two of the six you will now find a Hidden Twin. Complementary to them, the remaining four fields contain a Naked or Hidden Quadruplet. In this respect, the occurrence of the pattern is not uncommon.
But you wouldn't normally use this pattern in this situation. You'll find the twin faster, and the result usually opens up new options. The claim that this pattern is rare is based on a different scenario: You have tried all of the easier methods and none of them allow you to progress further. This makes searching for a Quadruplet (relatively) the last alternative.
"Relatively the last alternative" needs to be explained. First of all, the Quadruplet could have a complementary Quintuplet. And secondly, the Brute-Force method (see Chains and Loops) represents a viable alternative at any given time.
The images shown here are an attempt to show situations where the method explained above is relatively the last alternative. A Hexadoku has to suffice in this case. Due to its size , of course, it needs an extended symbol set (123456789abcdefg).
The yellow fields show a hidden Quadruplet with the candidates 1239.
A complementary Naked Quadruplet is also in the block, with the candidates 6afg.
The rules for elimination is the same for both methods.
see also: Generalization: Hidden groups